Mean field theory of the edge of chaos

Abstract

Is there art Edge of Chaos, and if so, can evolution take us to it? Many issues have to be settled before any definitive answer can be given. For quantitative work, we need a good measure of complexity. We suggest that convergence time is an appropriate and useful measure. In the case of cellular automata, one of the advantages of the convergence-time measure is that it can be analytically approximated using a generalized mean field theory. In this paper we demonstrate that the mean field theory for cellular automata can 1) reduce the variablity of behavior inherent in the λ-parameter approach, 2) approximate convergence time, and 3) drive an evolutionary process toward increasing complexity.